2 Answers
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No, it won't - 32bit OS can only use 4Gb RAM. And some of this will be reserved for the OS, giving you about 3GB RAM for your programs.

You need a 64bit OS to use more than 4GB RAM (assuming the software is also 64bit).

Furthermore, as per Michael Kjörling excellent comments, "Even if you use only 32-bit applications on a 64-bit OS, each application can get its own 4 GiB virtual address space. So even such an environment can benefit from >4 GiB RAM."

Even if you use only 32-bit applications on a 64-bit OS, each application can get its own 4 GiB virtual address space. So even such an environment can benefit from >4 GiB RAM.
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Michael KjörlingDec 19 '12 at 10:44

@MichaelKjörling - I agree, but, let's not confuse the OP :) Although thank you for the comment, I will include in my answer.
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DaveDec 19 '12 at 10:45

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A 32-bit application will only use more than 2 GB of user mode virtual address space if it is marked large address space aware. However the OP was asking about physical memory.
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David MarshallDec 19 '12 at 11:04

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@Offler - Except were not talking about Windows Server software we are talking about Windows 7 x86 and it only supports 4GB.
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RamhoundDec 19 '12 at 12:23

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@Offler - The user is not using a 10k+ operating system like Windows Server 2008 Datacenter Edition. Furthermore the comments I have made and others have made have been directed to 32-bit Windows 7 not Windows Server which ( by the way ) is no longer offered as a 32-bit operating system.
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RamhoundDec 19 '12 at 12:49

@RamHound they are completly wrong. look in the other comment.
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OfflerDec 19 '12 at 12:29

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@Offler - So your counter argument is PAE, you have to be kidding me, that causes all sorts of problems on your everyday desktop computer. As for hacking the kernel....You have to be kidding me.
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RamhoundDec 19 '12 at 12:37

No, my counter argument against the general " 32 bit os can only use 4GB" is: 1. there are still alot systems which can use more memory out of the box (like 2008 DataCenter, some Linuxes etc.pp". 2. Also on the other ones there are chances to enable it. It is no general rule of thumb that a 32 bit os can only use 4gb. and by the way: why do you think the server editions are still able to use PAE - and are normally used for more critical operations? From a long time back MS just does not want that consumer systems are used as servers (price). That as one of the main reasons.
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OfflerDec 19 '12 at 12:48